Chemistry

Chemistry

Problem

A sample of neon gas is confined in a rigid container whose volume does not change with temperature. The measured pressures at various Celsius temperatures are listed.
Temperature TT (∘C^{\circ}\text{C})0255075100
Pressure PP (kPa)98.0107.2116.0124.7133.5
Assume that the relationship between pressure and temperature is exactly linear over this range. (a) On appropriately labeled axes, sketch the graph of pressure PP versus temperature TT using the data in the table. (b) Determine the numerical slope and vertical intercept of the straight line that best fits the data. (c) Using your linear equation, calculate the temperature (in ∘C^{\circ}\text{C}) at which the pressure of the gas would be zero. (d) Express the temperature found in part (c) on the Kelvin scale.
Intuitive explanation

This problem tests Gay-Lussac's Law — the direct proportionality between pressure and absolute temperature for a gas at constant volume. The key insight is that you must convert Celsius to Kelvin before plotting or analyzing the relationship, since the gas laws depend on absolute temperature, not the arbitrary Celsius scale. Once you shift to Kelvin, the linear relationship will reveal the fundamental physics: pressure increases predictably because molecular collisions intensify as thermal energy rises.

Intuitive explanation

This problem tests Gay-Lussac's Law — the direct proportionality between pressure and absolute temperature for a gas at constant volume. The key insight is that you must convert Celsius to Kelvin before plotting or analyzing the relationship, since the gas laws depend on absolute temperature, not the arbitrary Celsius scale. Once you shift to Kelvin, the linear relationship will reveal the fundamental physics: pressure increases predictably because molecular collisions intensify as thermal energy rises.

Browse the problem library